A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$7.50$, and bags of cookies cost $$3.00$, and sales equaled $$45.00$ in total. There were $8$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Solution: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${7.5x+3y = 45}$ ${y = x+8}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+8}$ for $y$ in the first equation. ${7.5x + 3}{(x+8)}{= 45}$ Simplify and solve for $x$ $ 7.5x+3x + 24 = 45 $ $ 10.5x+24 = 45 $ $ 10.5x = 21 $ $ x = \dfrac{21}{10.5} $ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $ {y = x+8}$ to find $y$ ${y = }{(2)}{ + 8}$ ${y = 10}$ You can also plug ${x = 2}$ into $ {7.5x+3y = 45}$ and get the same answer for $y$ ${7.5}{(2)}{ + 3y = 45}$ ${y = 10}$ $2$ bags of candy and $10$ bags of cookies were sold.